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explicit construction of Morgenstern Ramanujan graphs for odd prime power q #17

@Fe-r-oz

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@Fe-r-oz

The Morgenstern construction for even prime power is enhanced, and tested in #16. However, this only implements the Theorem 5.13 which is regarding the construction of Ramanujan graphs using prime power q. Over the field $F_2$, we have the isomorphisms $GL_n(F_2) = SL_n(F_2) ≅ PGL_n(F_2) = PSL_n(F_2)$, because the center trivial. Hence, in the even construction, we use SL because the center is just the identity.

Section 4 (Theorem 4.13) is regarding the construction of these graphs using odd prime power q where we will work with both $PSL$ and $PGL$ without expensive center computation. Reference: here In addition, the work also assumes that q is even $q = 2^l$ before presenting alternative symmetric set of generators. The alternative set of generators is required to satisfy the total non-conjugacy condition.

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